Average Error: 0.3 → 0.2
Time: 4.7s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]
↓
\[\mathsf{fma}\left(y - x, 6 \cdot z, x\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot z
↓
\mathsf{fma}\left(y - x, 6 \cdot z, x\right)
double f(double x, double y, double z) {
        double r904993 = x;
        double r904994 = y;
        double r904995 = r904994 - r904993;
        double r904996 = 6.0;
        double r904997 = r904995 * r904996;
        double r904998 = z;
        double r904999 = r904997 * r904998;
        double r905000 = r904993 + r904999;
        return r905000;
}
↓
double f(double x, double y, double z) {
        double r905001 = y;
        double r905002 = x;
        double r905003 = r905001 - r905002;
        double r905004 = 6.0;
        double r905005 = z;
        double r905006 = r905004 * r905005;
        double r905007 = fma(r905003, r905006, r905002);
        return r905007;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.3
Target0.2
Herbie0.2
\[x - \left(6 \cdot z\right) \cdot \left(x - y\right)\]

Derivation

  1. Initial program 0.3

    \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]

  2. Simplified0.2

    \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot z, x\right)}\]

  3. Final simplification0.2

    \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot z, x\right)\]

Reproduce

herbie shell --seed 2020002 +o rules:numerics
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6 z) (- x y)))

  (+ x (* (* (- y x) 6) z)))